 Friends, starting from this lecture for the rest of the course we will be looking at the non-ideal reactors, how to characterize non-ideality in reactors. So in further we will be particularly looking at the distribution of residence time for chemical reactors, particularly we are looking at the distribution of residence time. Now it turns out that the ideal reactors that is the all the reactors that we have looked at so far they are all ideal reactors that is the plug flow and the mixed flow reactors. These are all ideal reactors and it turns out that the real world reactors they really do not behave like the plug flow or the mixed flow reactors. So the real world reactors are slightly different, real world reactors they behave differently and it is actually important to diagnose and understand when they deviate from ideal behavior. So we have seen how to write performance equations for ideal reactors like plug flow reactors or under mixed conditions and we have also we also know how to write performance equation for CSTR which is not necessarily an ideal situation, we will see what is meant by ideal situation and how where the CSTR fall into that category. So it is important to diagnose it is important to diagnose the deviation from the ideal behavior. So suppose if there is a reactor if I assume that it is a plug flow reactor and I write a performance equation and I find out what is the concentration profile of the reactor and let us say in the effluent that is after the stream leaves the reactor. Now the real world reactor perhaps may not attain that kind of a conversion and that sort of indicates that the reactor does not behave like a plug flow reactor. So the question is how do I diagnose such kind of a deviation. Now suppose if I have diagnosed such kind of a deviation and how do I characterize such a reactor which does not behave like the ideal reactor such as the plug flow and the mixed flow reactors. So the objective of the rest of the syllabus of the course is basically to look at analyze and analyze and characterize non-ideal reactor behavior. So that is going to be the objective for the rest of the course. So now the key piece of information that is actually used in order to analyze and characterize non-ideal reactor behavior is the distribution of residence time. Residence time distribution of a reactor quantifies the time spent by various fluid particles in the reactor and is a characteristic of mixing that occurs in the reactor. So in the rest of this lecture we are going to look at several examples of a non-ideal behavior that has been observed experimentally and observed in real systems and also look at some of the definitions of what is residence time and what are the different ways to capture the residence time distribution etc. So that is going to be the objective of this particular lecture. So the distribution of residence time is actually used to diagnose the reactor operation problems. It is also used to predict conversion of a new reaction when conducted in an existing reactor. So these two are important aspects if suppose if there is a reactor that is already being characterized. Now if you want to conduct a new reaction in that reactor is it possible to predict the behavior of that particular reaction in that reactor. So that is an important question and in addition to that suppose if there is an experiment that has been conducted in a small scale and then we want to scale it up to a next level to increase the productivity of that particular product which is desired then it is important to actually characterize the non-ideal behavior and it helps in scaling up the reactors. So let us look at a specific case of gas liquid CSTR. Suppose I take a tank and let us say that the gas A is being bubbled through the liquid. So let us say that the liquid is filled, let us say the tank is filled with liquid and bubble A is actually bubbled through this liquid inside and then it leaves the reactor from the top. So that is gas A which is actually entering from the bottom and it is being bubbled inside and then it leaves from the top of the reactor. Now suppose there is another liquid B which is now flowing through this reactor and the gas is simultaneously bubbled through this liquid. So the liquid leaves from the exit stream for the liquid. So now so A species A is actually being bubbled and species B is actually the liquid phase which is going through the reactor. So now one can actually realize that there are three processes which are actually occurring here. So remember this is a gas liquid reactor. So the reaction is actually occurring between the species A which is in the gas phase. The reaction is between species A in the gas phase and species B in the liquid phase and that leads to formation of certain products. So now if this reaction has to happen the species A which is present in the gas phase has to diffuse and come to the interface between the liquid and the gas stream. So the first process is the gas diffusion to the gas liquid interface. Now suppose I assume that the gas is immiscible in the liquid then the reaction has to occur at the gas liquid interface. So there is an interface between the gas stream which is present inside the bubbles and the fluid stream which is actually present around the bubbles and so therefore the gas species has to diffuse from the bulk inside the bubble to the gas liquid interface in order for it to get in contact with the liquid with which it has to react. And similarly, so this is basically diffusion of species A and similarly the species B has to actually undergo diffusion that should has to be a diffusion of species B to the gas liquid interface. So only after this these two processes have occurred the reaction between these two species can occur. So therefore the third step is the reaction between species A and species B at the gas liquid interface. It has been assumed that the reaction occurs at the interface however the reaction need not be confined to the interface as where the cases that were covered in lecture 26. So these are the three processes which are actually occurring in order for the reaction to actually occur. Now suppose we can assume that the liquid which is actually flowing from the top of the tank so as if you look at the tank again so the liquid which is actually flowing from the top of the tank through the tank and leaves the bottom of the liquid. So this is this can be assumed as a continuous liquid phase. So we can assume that the liquid is actually a continuous phase. So the liquid is actually continuously flowing continuously flowing and in fact it perhaps it can also be assumed that it is well mixed it can be assumed that it may be well mixed that is the concentration of the species in the liquid phase is almost uniform inside the reactor. Now that is not really true but may be we can assume for the time being that it is well mixed in order to actually appreciate what is happening inside the gas liquid CSTR and particularly in order to appreciate the nature of the non-ideal behavior. Although in reality even the liquid phase will not necessarily be well mixed but if it is a continuous phase and it may be assumed to be well mixed for the time being. So the question is what about gas phase? In fact comparing gas phase the liquid phase can actually easily be assumed as a well mixed phase. Now what about gas phase? Before we understand what happens in the gas phase let us try to actually understand how the what are the different properties that actually control the reaction rate. In fact it is that which gives an insight as to what is the nature of the fluid flow in the gas phase. So the reaction rate is actually proportional to the surface area. Suppose AB is the surface area of a particular bubble. So remember that the gas which is actually flowing from the bottom to and leaves the top of the reactor is actually bubbled inside. So it forms bubbles and then the bubbles raise inside the liquid stream and then while it raises the reaction occurs in the gas liquid interface and then the bubble leaves the reactor. So the reaction rate is actually proportional to the surface area of the bubble which is available for reaction. It is the surface area of the bubble which is actually available for the reaction to occur. Now the surface area of the bubble which is available for the reaction what does it depend upon? It actually depends upon the amount of time that the bubble actually spends inside the reactor. So therefore the surface area of the bubble available. So remember it is not the surface area just the surface area of the bubble it is the surface area of the bubble which is available for the reaction to occur when the bubble is actually rising from the bottom to the top of the reactor and that depends upon the time spent. So that depends upon the amount of time that the bubble actually spends inside the reactor. So the gas bubbles when it is actually generated when it is passed into the liquid they are generally not of same size so different gas bubbles are going to be of different sizes. So therefore so different size bubbles one can expect different size bubbles to be created and these different sizes are actually simultaneously they are raising up and because the bubbles are of different sizes different bubbles are going to raise at different velocities. So therefore clearly some bubbles may actually escape immediately. So some bubbles actually they will escape immediately which means as soon as they are created they will quickly go to the top of the liquid stream and then they will leave the reactor. And so the amount of time that these bubbles would have spent which have left immediately will be extremely small. Now others might spend more time other bubbles may spend more time inside the reactor and as a result of this the amount of species which is present in the gas phase can actually get completely consumed because the bubble is now spending sufficient time inside the reactor for all of the reactant to actually diffuse from the gas phase and reach the gas liquid interface and actually contact the liquid phase species in the liquid phase and the reaction to occur. So therefore some of these bubbles gets completely converted. So the gas species present in some of these bubbles gets completely converted. So there can be complete conversion or complete consumption of all the species in each of these bubbles. So when I say complete conversion it means that in one bubble which actually spends more time inside the reactor or in the bubble in bubble which actually spends more time inside the sufficiently more time inside the reactor. So that is what is meant by complete conversion in that particular bubble. So now as a result of this observation that different bubbles spend different amount of time inside the reactor and that some bubbles actually leave immediately and some bubbles actually spend more time in order for all the reactants present inside the bubble to have undergone reaction or to get consumed the gas phase cannot be assumed as well mixed cannot be considered as well mixed. So therefore it is important to consider the amount of time spent by the bubble inside the reactor while designing these kinds of gas liquid CSTRs. So just to define the time spent by the bubbles in the reactor is called bubble residence time that is called the bubble residence time that is the amount of time spent by bubble inside the reactor. Now as observed earlier different bubbles spend different time different bubbles spend different time inside the reactor and therefore different molecules of species A species A will have with different residence time. So different molecules of species A although all of them would have actually come into the reactor at the same time because of this feature that different bubbles spend different amount of time inside the reactor different molecules of species A would also have different residence time. So clearly this is going to affect the reaction rate. It is important to note that RTD affects the conversion but does not affect the intrinsic reaction kinetics why is that because the reaction rate is a function of the available surface area and the available surface area depends upon the amount of time that is actually spent by the bubbles inside the reactor. So therefore if different molecules of species A they have different residence time that is going to clearly affect the extent of the reaction it is going to affect the reaction rate. And therefore it is important to consider it is important to consider this aspect of different bubbles having different residence time into the model analysis. So therefore it is important to incorporate the bubble residence time in the analysis in the analysis of such reactor and moreover it is actually important it is need to consider it is important that one considers the individual bubble individual bubble residence time and not just the average. So it is not sufficient to consider only the average residence time of the bubbles it is important to consider the residence time of each and every bubble which is actually created because the bubble is being sparsed into the liquid. So and as a result the net reaction rate as a result the net reaction rate is simply going to be sum of the reaction rate in individual bubbles individual bubbles and summed over all bubbles. So if there are 100 bubbles inside the reactor then one needs to actually find out what is the reaction rate in each of these 100 bubbles and sum them all and that gives you the net reaction rate inside the reactor. Net reaction rate here refers to the observed total reaction rate and not the intrinsic reaction rate. So now let us look at another example of a packed bed reactor. So a packed bed reactor is nothing but a tube and the tube is packed with catalyst particles. So let us say that these are the catalyst particles which are actually present inside the reactor. So these are the catalyst particles which are actually packed inside and suppose if a fluid stream is actually flowing into the reactor let us say that it has a flat profile that means the velocity with which the fluid is actually flowing and the concentration with which the fluid is actually entering the stream is actually uniform across a given cross section. So suppose if it flows uniformly inside then because of the packing the resistance to flow is not going to be uniform at every location in a given cross section. So therefore one can observe that the fluid stream is now going to bend and then it is going to move through the crevices of the reactor and then they are going to leave from the other side. So clearly one can observe that the fluid behavior is not going to be uniform. So clearly the fluid flow is going to be a non-uniform fluid flow and why would that be the case? So some sections can actually offer more resistance. So some sections will offer more resistance to flow and as a result the channeling of fluids will occur. So as depicted here in some sections of the reactor the fluid will actually quickly go from the inlet to the exit of the reactor and leave the reactor while in the other sections they spend a lot more time. So clearly the amount of time that is spent by different molecules of the species that is entering the reactor is going to be different. Which means that there is going to be a distribution of residence time that is clearly going to be a distribution of residence time of the molecules which are actually entering the reactor and is participating in the reaction. So let us take another example of CSTR, a well mixed CSTR. Suppose we take a well mixed CSTR, so CSTR is a tank, that is a tank and it has a mixer. So let us assume that it is rotating in this direction and if the species is actually entering through, entering into the reactor, suppose this is the feed stream, species A is entering into the reactor at the feed, via the feed stream and let us say that the outlet of this reactor is at this location. So this is the out and this is the in stream and what happens is that often the inlet and the outlet streams of the reactor may actually be placed close to each other for various reasons and because of that what happens is that some of the fluids would actually quickly, some of the fluid that is entering the CSTR would actually quickly leave the reactor and in fact that process is called as bypassing. So the, some of the fluid particles which are actually entering into the reactor would actually bypass and leave the reactor and as a result what is created is some of the, some locations of the reactor are actually underutilized or unutilized and those zones are called as the dead zones. So what has been observed is that the, there is bypassing of fluid stream and because the inlet and outlet may be placed close to each other and so some of the fluid particles will quickly bypass and of course if one needs to model such kind of a reactor this has to be incorporated in the model and the second problem is the presence of a dead zone where the reactants are actually where the, where there is no reaction occurring in the dead zone so there is no reaction and not just that there is no reaction there is actually no exchange of materials from the dead zone to the well-mixed zone. So in addition to that no exchange of material from dead zone to, from dead zone to well-mixed zone. So clearly this suggests that there will be a distribution of residence time. So there will be distribution of residence time even in the case of where there is a CSTR with bypassing occurring inside the reactor. So all these three examples are actually a good motivation to think that there is a requirement for strategies to handle non-ideal behavior. So it is important to come up with strategies to handle the non-ideal behavior of reactors and this is very common because the ideal reactor such as the plug flow and the mixed flow reactors are commonly the not, they are not a good representation of the real world reactors. They do not behave exactly like the plug flow and the mixed flow and in fact we will see in one of the, in the future lectures that the one can actually clearly show using the residence time distribution that the real reactors do not necessarily behave like a plug flow or the mixed flow. So there are three concepts which are involved here. There are three concepts that one need to understand in order to come up with strategies to handle the non-ideal behavior of reactors. So the first one on that is the residence time distribution. So that is the amount of time that is actually spent by a given fluid particle inside the reactor and the distribution says how much time different fragments of the fluid particles are actually spending time inside the reactor. Then the second important aspect is the quality of mixing. So what is the extent of mixing that is actually undergoing inside the reactor due to various reasons. So one needs to understand and characterize the nature of extent of mixing in order to be able to understand the non-ideal behavior of reactors. And then the third aspect is basically to model used to describe such systems. So one needs to come up with ways by which one can actually model such kind of non-ideal behavior and so we are going to see that what are the various ways by which we can actually characterize the non-ideal behavior using these three concepts. And several examples will actually be shown to explain each of these concepts. And in fact, the RTD, the residence time distribution, it actually is used to describe, it describes the deviation from non-ideal behavior, from ideal behavior. So the residence time distribution actually describes the deviation or it sort of captures the deviation from the ideal flow behavior and we are going to look at how it captures in a short while. So the first step towards handling this, handling a real world reactor that is the actual reactor which may be present in an industry. So the first step is basically to model them as an ideal reactor. So the first step is to assume that the reactor is an ideal reactor. What it means is that it needs to be modeled either as a PFR or a CSTR. So one can actually model it as a plug flow reactor or a CSTR reactor. Remember that even in a CSTR, the residence time is not same for all the particles that actually goes through the reactor. However, it is a thoroughly perfectly well-mixed system. So it has certain ideal properties and we will see in a short while how to characterize them. And then suppose if this model does not predict the actual behavior of the reactor, then one needs to actually introduce the non-ideal behavior that is the non-ideal flow pattern. One needs to introduce the non-ideal flow pattern and in fact, in order to introduce a non-ideal flow pattern, one has to actually account for the ineffective contacting. While some of these fluid, for example, let us take the packed bed reactor case. The some of the fluid actually enters and leaves the reactor immediately because of the channeling effect. And so the contact that actually these fluid stream has with the catalyst particles present inside the reactor is not very effective. And therefore, one needs to account for such kind of ineffective contacting and also one needs to account for low conversion compared to ideal reactors. So one needs to account for these two factors if one has to introduce the non-ideal behavior into the ideal reactor model. So once we know once we know that the reactor behaves like a non-ideal reactor, then we need to account these two aspects into the model to capture the dynamics or the behavior of the reactor. Now the question is how do we account these two factors? So the first, so one needs to actually look at the macro mixing, macro mixing which is basically the residence time distribution which captures the macro mixing. One needs to account for macro mixing in the system and the other aspect is the micro mixing that is the, so this is the mixing at micro scale. So one needs to account for these two factors and in fact these two factors will actually help in characterizing the non-ideal behavior of the reactor. So let us first look at the residence time distribution which actually account for the macro mixing. So the residence time distribution was actually originally proposed by MacMullin and Weber in 1935. However it was actually ignored for nearly two decades and later Danckwerts came and actually gave a special structure to the residence time distribution and defined various types of possible distributions. So it was Danckwerts in 1953 gave structure to RTD. In fact he came and took the idea of MacMullin and Weber and developed it further and gave some special structure to RTD. Therefore most of the RTD work is actually attributed to the seminal work done by Danckwerts in 1953. So now we said that the plug flow reactor is an ideal reactor. So why is it an ideal reactor? So let us look at the ideal plug flow reactor. So plug flow reactor can actually be an ideal reactor under certain situations. So what are the properties of an ideal plug flow reactor? So in an ideal plug flow reactor all atoms and material, all atoms of the material have same residence time. So suppose there is a fluid which is actually flowing through a plug flow reactor then all fluid particles that actually entering the ideal plug flow reactor they spend exactly the same amount of time inside the reactor before they leave the plug flow reactor. So that is an important characteristic of an ideal plug flow reactor. And what about an ideal batch reactor? What about ideal batch reactor? So ideal batch reactor is one where all atoms inside has been in the reactor for same time. So all atoms that are actually present inside the batch reactor, ideal batch reactor they actually have been there, all atoms have been there for exactly the same amount of time as each other. And so therefore the time that is actually spent by these atoms inside the reactor is called the residence time and both these ideal plug flow reactor and the ideal batch reactor they actually have all the molecules inside they have exactly the same residence time. So there are actually only two classes of ideal reactors. In fact there are only two classes of reactors in which the residence time can actually be same. So it is the ideal plug flow and the ideal batch reactors, two classes with same residence time. So all other reactors there is going to be a distribution of residence time including CSTR. So suppose what happens in a CSTR, CSTR is something that has been commonly studied in this course in many different in the first course of the reaction engineering. And so what happens in a CSTR? How can we describe what is the nature of the residence time distribution in a CSTR? So suppose if we take a tank and then we feed a certain species into the tank which is undergoing a reaction. So if we consider the feed at a particular time, suppose we look take the feed at a particular time, suppose we consider feed at a certain time then as the feed stream actually enters into the reactor, the feed stream because it is a CSTR the feed stream immediately gets completely mixed with the materials which are already present inside the reactor. Now not just that the there may be a small fraction of the feed stream which is actually carried along with the fluid stream and it leaves the reactor. So therefore it is possible that some fluid stream, some fluid stream leaves immediately, some fluid stream actually leaves immediately. And so therefore the residence time of these fluid stream which actually leave the reactor immediately is going to be very small and in fact it is going to be different as compared to the residence time of others be other particles which are actually staying inside the reactor. So other particles they are going to stay for a much longer time and in fact most of the particles it has been observed that most of spend approximately the mean residence time. So most of the fluid particles the amount of time they spend inside the reactor is approximately equal to the mean residence time. So therefore the residence time distribution actually characterizes the extent of mixing. So in a CSTR the some fluid stream leaves immediately and the other they stay for a longer time which means that there is going to be a distribution and in fact the residence time distribution it characterizes the extent of mixing inside the reactor. So that is an important aspect it is a characteristic of mixing. So residence time distribution henceforth will be referred to as RTD and it is actually a characteristic of the mixing which is happening inside the reactor. So now if I take a plug flow reactor there is no axial mixing in a plug flow reactor. There is no axial mixing in a plug flow reactor which means that the if there is a tube and if it behaves like a plug flow reactor then the fluid stream which is actually entering inside they actually move like a plug which means that the fluid particles which is actually entering the reactor at a certain time they do not mix with the fluid particles which are actually entering just after it or just before it. So therefore there is no axial mixing of fluid particles inside the reactor if it behaves like a plug flow reactor and this can actually be seen this behavior or this aspect of no axial mixing can actually be seen in the residence time distribution. And it will be shown in one of the lectures in the one of the future lectures that for a plug flow reactor there is actually no axial mixing and that can be deciphered from the residence time distribution curve itself. And let us look at CSTR. So the CSTR is actually thoroughly mixed which means that the concentration of the species inside the reactor is going to be uniform at all times and so it is a thoroughly mixed system and that can also be seen in the residence time distribution of the reactor. So now and in fact one will observe which we will see in one of the future lectures is that the RTD of CSTR is actually very different from. So the residence time distribution observed for a CSTR is going to be very very different from the residence time distribution of a plug flow reactor. So at this point one needs to also know that not all residence time distributions are actually unique to the reactor type. So it does not mean that every reactor type has a unique residence time distribution and there is no 1 to 1 correlation, there is no one residence time distribution for a particular reactor type. So what it means is that different reactors can actually show identical residence time distribution. In fact different reactors of completely different configuration they can also very very similar residence time distribution. So residence time distribution can actually be used to decipher the nature of the functioning of that particular reactor or nature of the non-ideality that is present inside the reactor. So now the question is how do we detect these non-ideal behavior, how do we detect the residence time distribution experimentally. So it is actually possible to measure, it is possible to measure the residence time distribution and in fact it is experimentally determined using what is called a tracer. So suppose if there is a reactor a fluid stream is flowing through this reactor which is actually participating in a certain reaction which is getting consumed to form products. Now in order to find out what is the residence time distribution, in order to detect whether the reactor is ideal or non-ideal we need to know what is the residence time distribution and the way to do that is basically to use a tracer. So what is done is at time t equal to 0, so a tracer is introduced. So a tracer chemical is actually introduced and then monitor the tracer concentration as a function of time in a fluid. So one can actually measure the tracer concentration that actually is going to flow along with the fluid. So the tracer is introduced at the inlet of the reactor and the tracer is now going to be taken forward, taken by the fluid along the reactor and it is going to leave the reactor. So one can actually measure the concentration of the tracer material as it leaves the reactor and that way one can actually construct the residence time distribution. Now it is not possible to conduct such an experiment with any kind of tracer. The tracer has to have certain properties. So for example the tracer must actually satisfy certain important, must have certain important properties in order for it to be used to measure the residence time distribution and these properties are basically they have to be non-reactive species, they have to be non-reactive otherwise is going to get consumed inside the, otherwise is going to get consumed because of some reaction and if it gets consumed then one cannot observe the non-ideal behavior or non-ideal flow pattern using this particular tracer and then it must be easily deductible. So the tracer chemical must be easily deductible that means that there must be methodologies well established methodologies in order to measure the concentration of the tracers in a very short time which means that the equipments must be sensitive enough to distinguish the small concentrations of the tracers. The physical properties should be such that similar to that of the reacting mixtures. So if the physical properties are not similar then it does not reflect the exact flow behavior of the reacting mixture which is of interest to actually study. So now in addition to that it must also be completely soluble, it must be completely soluble in the reacting mixture and it actually should not absorb to wall or any other surface of the reactor. So it should not absorb to wall or any other surface because if it gets absorbed then the sum of the species are being consumed and that is not going to help in actually measuring the residence time distribution of the reactor. So typically colored and radioactive materials along with inert gas are actually commonly used as tracers. So inert gas with some colored and radioactive material. So these are all commonly used tracers for actually finding the residence time distribution. So there are actually two common strategies for injecting the tracer. So two strategies for methods. So there are two methods for injecting the tracer in order to study the residence time distribution. The first one is the pulse input and the second one is the step input. So these are the two classical methods of tracer injection in order to detect the residence time distribution. So which is what we will see in the next lecture and what we have seen today is basically to introduce what is the non-ideal behavior and that to appreciate that the real world reactors do not behave like the ideal reactors such as the plug flow and the mixed flow reactors that we have studied in the in the past. And what are the definitions that is the residence time distribution definitions that are actually involved to characterize such kind of non-ideal behavior. So what we will see in the next lecture is to look at what is this pulse input and the step input method in order to track the residence time distribution of a given system. Thank you.